Luke, Ken and Ben had some coins in the ratio of 4 : 5 : 9. Ben gave 40% of his coins to Luke and Ken. As a result, Luke had the same number of coins as Ken and Ben had 45 fewer coins than Luke.
- What was the percentage increase in Luke's coins after receiving from Ben?
- How many coins did Ken have at first?
| Luke |
Ken |
Ben |
Total |
| 4 u |
5 u |
9 u |
18 u |
| + 3.6 u |
- 3.6 u |
|
| 6.3 u |
6.3 u |
5.4 u |
18 u |
(a)
Number of coins that Ben gave away
= 40% x 9
=
40100 x 9
= 3.6 u
Number of coins that Luke and Ken each had in the end
= (18 u - 5.4 u) ÷ 2
= 12.6 u ÷ 2
= 6.3 u
Increase in the number of coins that Luke had
= 6.3 u - 4 u
= 2.3 u
Percentage increase in Luke's coins after receiving from Ben
=
2.34 x 100%
= 57.5%
(b)
6.3 u = 5.4 u + 45
6.3 u - 5.4 u = 45
0.9 u = 45
1 u = 45 ÷ 0.9 = 50
Number of coins that Ken had at first
= 5 u
= 5 x 50
= 250
Answer(s): (a) 57.5%; (b) 250
